IXL - Find one-sided limits using graphs (Calculus practice)

Use the graph to find

lim

→9

(

)

lim

→9

(

)

ref_doc_title.

Learn with an example

question

Use the graph to find

lim

→1

(

)

lim

→1

(

)

key idea

The limit

lim

→

(

)

is what the values of

(

)

approach as

approaches

from the

left.

This limit may or may not exist. It is also called the left-hand limit of

(

)

This graph shows an example where

lim

→

(

)

exists.

The limit

lim

→

(

)

is what the values of

(

)

approach as

approaches

from the

right.

This limit may or may not exist. (The value of the limit doesn't have to be the same as the value of the function for the limit to exist.) It is also called the right-hand limit of

(

)

This graph shows an example where

lim

→

(

)

exists.

solution

The limit

lim

→1

(

)

has a raised minus sign after the 1. This means it is the left-hand limit of

(

)

at 1. To find the limit, look at the values of

(

)

approaches 1 from the left.

approaches 1 from the left,

(

)

approaches

–

So,

lim

→1

(

)

–

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A.1Find limits using graphs

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